Skip to main content Accessibility help

Polynomial chaos assessment of design tolerances for vortex-induced vibrations of two cylinders in tandem

  • Gianluca Geraci (a1), Marco Donato De Tullio (a2) and Gianluca Iaccarino (a1)


The presence of aerodynamics loadings makes the design of some classes of elastic structures, as, for instance, marine structures and risers, very challenging. Moreover, capturing the complex physical interaction between the structure and the fluid is challenging for both theoretical and numerical models. One of the most important phenomena that appear in these situations is vortex-induced vibrations. The picture is even more complicated when multiple elastic elements are close enough to interact by modifying the fluid flow pattern. In the present work, we show how the common design practice for these structures, which is entirely based on deterministic simulations, needs to be complemented by the uncertainty quantification analysis. The model problem is a structure constituted by two elastically mounted cylinders exposed to a two-dimensional uniform flow at Reynolds number 200. The presence of a manufacturing tolerance in the relative position of the two cylinders, which we consider to be a source of uncertainty, is addressed. The overall numerical procedure is based on a Navier–Stokes immersed boundary solver that uses a flexible moving least squares approach to compute the aerodynamics loadings on the structure, whereas the uncertainty quantification propagation is obtained by means of a nonintrusive polynomial chaos technique. A range of reduced velocities is considered, and the quantification, in a probabilistic sense, of the difference in the performances of this structure with respect to the case of an isolated cylinder is provided. The numerical investigation is also complemented by a global sensitivity analysis based on the analysis of variance.


Corresponding author

Reprint requests to: Gianluca Geraci, Flow Physics and Computational Engineering, Stanford University, Building 500, Room 500A, 488 Escondido Mall, Stanford, CA 94305-3035, USA. E-mail:


Hide All
Borazjani, I., & Sotiropoulos, F. (2009). Vortex induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region. Journal of Fluid Mechanics 621, 321364.
Creastaux, T., Le Maître, O., & Martinez, J.M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety 94(7), 11611172.
Det Norske Veritas. (2009). Riser Interference. DNV Recommended Practice F203. Oslo: Author.
de Tullio, M.D., Cristallo, A., Balaras, E., & Verzicco, R. (2009). Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve. Journal of Fluid Mechanics 622, 259290.
de Tullio, M.D., & Pascazio, G. (2016). A moving least-squares immersed boundary method for simulating the fluid-structure interaction of elastic bodies with arbitrary thickness. Journal of Computational Physics 325, 201225.
de Tullio, M.D., Pascazio, G., & Napolitano, M. (2012). Arbitrarily shaped particles in shear flow. Proc. 7th Int. Conf. Computational Fluid Dynamics (ICCFD7), Hawaii, July 913.
Geraci, G., Congedo, P.M., Abgrall, R., & Iaccarino, G. (2016). High-order statistics in global sensitivity analysis: decomposition and model reduction. Computer Methods in Applied Mechanics and Engineering 301, 80115.
Geraci, G., de Tullio, M.D., & Iaccarino, G. (2015). Stochastic analysis of vortex-induced vibrations of two oscillating cylinders in the proximity-wake interference region. Annual Research Briefs, pp. 197–210. Stanford, CA: Sanford University, Center for Turbulence Research.
Griffin, O.M., & Ramberg, S.E. (1982). Some recent studies of vortex shedding with application to marine tubulars and risers. Journal of Energy Resources Technology 104(1), 213.
Hammings, R.W. (1959). Stable predictor–corrector methods for ordinary differential equations. Journal of the ACM 6, 3747.
Liu, G., & Gu, Y.T. (2005). An Introduction to Meshfree Methods and Their Programming. Dordrecht: Springer.
Lucor, D., & Triantafyllou, M.S. (2008). Parametric study of a two degree-of-freedom cylinder subject to vortex induced vibrations. Journal of Fluids and Structures 24, 12841293.
Mittal, R., & Iaccarino, G. (2005). Immersed boundary methods. Annual Review of Fluid Mechanics 37, 239261.
Sobol, I.M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55, 271280.
Swartzrauber, P.N. (1974). A direct method for the discrete solution of separable elliptic equations. SIAM Journal of Numerical Analysis 11, 11361150.
Uhlmann, M. (2005). An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics 209, 448476.
Vanella, M., & Balaras, E. (2009). A moving-least squares reconstruction for embedded-boundary formulations. Journal of Computational Physics 228, 66176628.
Verzicco, R., & Orlandi, P. (1996). A finite difference scheme for three-dimensional incompressible flows in cylindrical coordinates. Journal of Computational Physics 123, 402413.
Wiener, N. (1938). The homogeneous chaos. American Journal of Mathematics 60(4), 897936.
Williamson, C.H., & Govarghan, R. (2004). Vortex induced vibrations. Annual Review of Fluid Mechanics 36, 413455.
Williamson, C.H., & Roshko, A. (1988). Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures 2, 355381.
Xiu, S., & Karniadakis, G.E. (2002). The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing 24(2), 619644.
Xiu, S., Lucor, D., Su, C.H., & Karniadakis, G.E. (2002). Stochastic modeling of flow-structure interactions using generalized polynomial chaos. Journal of Fluids Engineering 124, 5159.
Yang, J., & Balaras, E. (2006). An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries Journal of Computational Physics 215, 1240.
Zdravkovich, M.M., & Pridden, D.L. (1977). Interference between two circular cylinders, series of unexpected discontinuities. Journal of Wind Engineering and Industrial Aerodynamics 2, 255270.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed